Problem: Rewrite as a simplified fraction. ${0.5\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 54.4444...\\ 10x &= 5.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 49}$ ${x = \dfrac{49}{90}} $